A review of maximum-norm a posteriori error bounds for time-semidiscretisations of parabolic equations

2022/12/22 by Torsten Linß, Linß, Torsten, Natalia Kopteva +5
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2212.11540

Abstract

A posteriori error estimates in the maximum norm are studied for various time-semidiscretisations applied to a class of linear parabolic equations. We summarise results from the literature and present some new improved error bounds. Crucial ingredients are certain bounds in the L₁ norm for the Green's function associated with the parabolic operator and its derivatives.

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